Gaussian Process Regression Model for Damage Localization in Plates Based on Modal Data

Document Type : Regular Paper


Department of Civil Engineering, Azarbaijan Shahid Madani University, Tabriz, Iran


The applications of plate like structures in different fields of engineering are increasing. In this paper, a new damage detection method investigated based on Gaussian process regression model (GPR). GPR is an efficient learning machines which has been used in different fields of engineering. To identify damage, mode shaped and natural frequencies of damaged structures used to train GPR. Finite element modelling of numerical examples and Gaussian process regression (GPR) model are carried out within the MATLAB environment. To show the effectiveness of presented approach, a two-fixed supported plate and a cantilever plate was studied. In other work, a comparative study has been done using a cantilever plates. The natural frequencies were contaminated with noise in above mentioned numerical examples. Results reveal that the proposed method works well using the only first mode data which may be noisy. In other word, GPR can be trained using limited sample numbers for training.


Main Subjects

[1] Doebling, S. W., Farrar, C. R., & Prime, M. B. (1998). “A summary review of vibration-based damage identification methods”, Shock and vibration digest, Vol. 30, No. 2, pp. 91-105.
[2] Lale Arefi, S., Gholizad, A., Seyedpoor, S. (2010). “Damage Detection of Structures Using Modal Strain Energy with Guyan Reduction Method”, Journal of Rehabilitation in Civil Engineering, Vol. 8, No.4, pp. 47-60. doi:
[3] Kourehli, S. S. (2020). “Damage Identification of Structures Using Second-Order Approximation of Neumann Series Expansion”, Journal of Rehabilitation in Civil Engineering, Vol. 8, No. 2, pp. 81-91. doi:
[4] Seyedi SR, Keyhani A, Jahangir H (2015) “An Energy-Based Damage Detection Algorithm Based on Modal Data.” In: 7th International Conference on Seismology & Earthquake Engineering. International Institute of Earthquake Engineering and Seismology (IIEES), pp 335–336.
[5] Bagheri, A., Amiri, G. G., Khorasani, M., & Bakhshi, H. (2011). “Structural damage identification of plates based on modal data using 2D discrete wavelet transform”, Structural Engineering and Mechanics, Vol. 40, No. 1, pp. 13-28.
[6] Hu, H., & Wu, C. (2009). “Development of scanning damage index for the damage detection of plate structures using modal strain energy method”, Mechanical Systems and Signal Processing, Vol. 23, No. 2, p. 274-287.
[7] Xiang, J., & Liang, M. (2012), “A two-step approach to multi-damage detection for plate structures”, Engineering Fracture Mechanics”, Vol. 91, pp. 73-86.
[8] Rucevskis, S., Akishin, P., & Chate, A. (2015). “Numerical and Experimental Study on the Application of Mode Shape Curvature for Damage Detection in Plate-Like Structures”, Solid State Phenomena, Vol. 220, pp. 264-270.
[9] Saeed, R. A., Galybin, A. N., & Popov, V. (2012). Crack identification in curvilinear beams by using ANN and ANFIS based on natural frequencies and frequency response functions, Neural computing and applications, Vol. 21, No.7, pp. 1629-1645.
[10] Kourehli, S. S., Bagheri, A., Ghodrati Amiri, G., Ghafory-Ashtiany, M., (2014). “Structural damage identification method based on incomplete static responses using an optimization problem”, Scientia Iranica, Vol. 21, No. 4, pp. 1209-1216.
[11] Rasouli, A., Ghodrati Amiri, G., Kheyroddin, A., Ghafory-Ashtiany, M., Kourehli, S. S. (2014). “A New Method for Damage Prognosis Based on Incomplete Modal Data via an Evolutionary Algorithm”, European Journal of Environmental and Civil Engineering, Volume 18, No. 3, pp. 253-270.
[12] Kourehli, S. S. (2015), “Damage quantification method using artificial neural network and static response with limited sensors”, Journal of Vibroengineering, Vol. 17, No. 3, pp. 1317‑1325.
[13] Kourehli, S. S. (2016). “LS-SVM Regression for Structural Damage Diagnosis Using the Iterated Improved Reduction System”, International Journal of Structural Stability and Dynamics, Vol. 16, No. 6, 1550018.
[14] Ghadimi, S., Kourehli, S. S. (2017). “Multiple Crack Identification in Euler Beams Using Extreme Learning Machine”, KSCE journal of civil engineering, Vol.21, pp. 389-396.
[15] Xu, Q. (2013). “Impact detection and location for a plate structure using least squares support vector machines”, Structural Health Monitoring, 1475921713495083.
[16] Fu, H. and Xu, Q. (2013). “Locating impact on structural plate using principal component analysis and support vector machines”, Mathematical Problems in Engineering, DOI: 10.1155/2013/352149.
[17] Naderpour, H., and P. Fakharian. "A synthesis of peak picking method and wavelet packet transform for structural modal identification." KSCE Journal of Civil Engineering 20, no. 7 (2016): 2859-2867.
[18] Keprate, A., Ratnayake, R. C., & Sankararaman, S. (2017). Adaptive Gaussian process regression as an alternative to FEM for prediction of stress intensity factor to assess fatigue degradation in offshore pipeline. International Journal of Pressure Vessels and Piping, 153, 45-58.
[19] Kourehli, S. S. (2018). Plate-like structures damage detection based on static response and static strain energy using gaussian process regression (GPR). Inverse Problems in Science and Engineering, 26(8), 1198-1213.
[20] Rasmussen, C. E. and C. K. I. Williams. (2006). “Gaussian Processes for Machine Learning”, MIT Press. Cambridge, Massachusetts.
[21] MATLAB, (2013). Matlab User Manual, Mathwork Inc. Lowell, MA, U.S.A.
[22] Amiri, G. G., Seyed Razzaghi, S. A. and Bagheri A., (2011). “Damage detection in plates based on pattern search and genetic algorithms”, Smart Structures and Systems, Vol. 7, No. 2, pp. 117-132.Department of Civil Engineering, Azarbaijan Shahid Madani University, Tabriz, Iran